A holographic recording system is built under incoherent light illumination based on a spatial light modulator and the mathematical model of the system has been established, then we get the specific forms of the point spread function, the axial magnification and the reconstruction distance. The experiments give the three phase-shift holograms and its reconstruction of a negative test slide. Then the holograms of two non-fluorescent dice are captured and digital reconstructed in different planes. The color holographic results are also given. The results show that the system can obtain holograms of real objects simply and rapidly. And we can get a clearly reconstruction without the zero-order and twin image by using the phase-shift algorithm.